Right of appeal to highest appellate authority allows challenges to assessing authority orders and grants conditional stay powers. A person aggrieved by assessing authority orders under section 6A may appeal to the highest appellate authority of the State, raising incidental issues like rate of tax, assessable turnover and penalty. Such appeals must be filed within the prescribed period; certain pending appeals are transferable and treated as appeals under this provision. The highest appellate authority may, after hearing both parties, pass appropriate orders, endeavor to decide within the prescribed timeframe, and grant conditional stays subject to terms including directions for deposits toward assessed tax.